# Unbounded Violation of Tripartite Bell Inequalities

@article{PrezGarca2007UnboundedVO, title={Unbounded Violation of Tripartite Bell Inequalities}, author={David P{\'e}rez-Garc{\'i}a and Michael M. Wolf and Carlos Palazuelos and Ignacio Villanueva and Marius Junge}, journal={Communications in Mathematical Physics}, year={2007}, volume={279}, pages={455-486} }

We prove that there are tripartite quantum states (constructed from random unitaries) that can lead to arbitrarily large violations of Bell inequalities for dichotomic observables. As a consequence these states can withstand an arbitrary amount of white noise before they admit a description within a local hidden variable model. This is in sharp contrast with the bipartite case, where all violations are bounded by Grothendieck’s constant. We will discuss the possibility of determining the… Expand

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#### References

SHOWING 1-10 OF 91 REFERENCES

Bell inequality with an arbitrary number of settings and its applications

- Physics
- 2006

Based on a geometrical argument introduced by Zukowski, a new multisetting Bell inequality is derived, for the scenario in which many parties make measurements on two-level systems. This generalizes… Expand

Aspects of Generic Entanglement

- Mathematics, Physics
- 2006

We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the ``concentration… Expand

Extremal quantum correlations for N parties with two dichotomic observables per site

- Physics, Mathematics
- 2005

Consider a scenario where $N$ separated quantum systems are measured, each with one among two possible dichotomic observables. Assume that the $N$ events corresponding to the choice and performance… Expand

Grothendieck's constant and local models for noisy entangled quantum states

- Physics
- 2006

We relate the nonlocal properties of noisy entangled states to Grothendieck's constant, a mathematical constant appearing in Banach space theory. For two-qubit Werner states rho p W… Expand

Multiplicativity of Completely Bounded p-Norms Implies a New Additivity Result

- Mathematics, Physics
- 2006

AbstractWe prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ12) − S(γ1)… Expand

Bell’s inequalities and distillability in N -quantum-bit systems

- Physics
- 2002

The relation between Bell inequalities with two two-outcome measurements per site and distillability is analyzed in systems of an arbitrary number of quantum bits. We observe that the violation of… Expand

Entanglement versus bell violations and their behavior under local filtering operations.

- Mathematics, Medicine
- Physical review letters
- 2002

The optimal local filtering operations leading to the maximal Bell violation for a given state are provided, and the special role of the resulting Bell diagonal states in the context of Bell inequalities is discussed. Expand

Separable balls around the maximally mixed multipartite quantum states

- Physics
- 2003

We show that for an m-partite quantum system, there is a ball of radius 2{sup -(m/2-1)} in Frobenius norm, centered at the identity matrix, of separable (unentangled) positive semidefinite matrices.… Expand

Experimental violation of a Bell's inequality with efficient detection

- Physics, Medicine
- Nature
- 2001

Here, correlations in the classical properties of massive entangled particles (9Be+ ions): these correlations violate a form of Bell's inequality, and the high detection efficiency of the apparatus eliminates the so-called ‘detection’ loophole. Expand

Experimental violation of a cluster state bell inequality.

- Physics, Medicine
- Physical review letters
- 2005

It is experimentally demonstrate that correlations in a four-qubit linear cluster state cannot be described by local realism, and a cluster-state Bell parameter of 2.59+/-0.08 is observed, which is more than 7sigma larger than the threshold of 2 imposed byLocal realism. Expand